A wide literature uses date of birth as an instrument to study the causal effects of educational attainment. This paper shows how parents delaying their children's initial enrollment in kindergarten, a practice known as redshirting, can make estimates obtained through this identification framework all but impossible to interpret. A latent index…

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the "significance region," or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA),…